A sum of Rs 5000 becomes Rs 8000 in 3 years, when invested in a scheme of simple interest. If the same sum is invested in a scheme of compound interest with same yearly interest rate (compounding of interest is yearly), then what will be the amount (in Rs) after 3 years?

Principal sum = Rs. 5000 and time period = 3 years

=> Amount after simple interest = Rs. 8000

Thus, simple interest = Rs. (8000-5000) = Rs. 3000

Let rate of interest = $$r\%$$

=> Simple interest = $$\frac{P\times R\times T}{100}$$

=> $$\frac{5000\times r\times3}{100}=3000$$

=> $$150r=3000$$

=> $$r=\frac{3000}{150}=20\%$$

$$\therefore$$ Amount under compound interest = $$P(1+\frac{R}{100})^T$$

= $$5000(1+\frac{20}{100})^3$$

= $$5000(1+\frac{1}{5})^3=5000(\frac{6}{5})^3$$

= $$5000\times\frac{216}{125}$$

= $$40\times216=Rs.$$ $$8640$$

=> Ans - (A)